Question 709: Electrostatics & Capacitance

Question

A charge $$\mathrm{Q} ~\mu \mathrm{C}$$ is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit) :

Accepted Answer

The Gaussian surface for the charge placed at the center of the cube will spread out equally through all sides of the cube. According to Gauss's Law, electric flux $$\Phi$$ through a closed surface is equal to the charge enclosed $$Q$$ divided by the permittivity of free space $$\epsilon_0$$:
$$\Phi_{	ext{total}} = \frac{Q}{\epsilon_0}$$
Given that the cube has 6 faces, and due to symmetry, the flux through each face will be equal, the flux through any one face $$\Phi_{	ext{face}}$$ is:
$$\Phi_{	ext{face}} = \frac{\Phi_{	ext{total}}}{6} = \frac{Q}{6\epsilon_0}$$
Since the charge is given in microcoulombs ($$\mu\mathrm{C}$$), we need to convert it to coulombs by multiplying with $$10^{-6}$$:
$$\Phi_{	ext{face}} = \frac{Q 	imes 10^{-6}}{6\epsilon_0}$$
This matches option D, which means the correct flux through one face of the cube given a charge Q microcoulombs at the center is $$\frac{Q}{6\epsilon_0} 	imes 10^{-6}$$.

Answer

$$\frac{Q}{\epsilon_0} 	imes 10^{-6}$$

Answer

$$\frac{2 \mathrm{Q}}{3 \epsilon_0} 	imes 10^{-3}$$

Answer

$$\frac{\mathrm{Q}}{6 \epsilon_0} 	imes 10^{-3}$$

Answer

$$\frac{\mathrm{Q}}{6 \epsilon_0} 	imes 10^{-6}$$

Electrostatics & Capacitance

A charge $\mathrm{Q} ~\mu \mathrm{C}$ is placed at the centre of a cube. The flux coming out from any one of its faces will be (in SI unit) :

Choose the correct answer: